5. The following sample observations on total coating layer thickness (in mm) of eight wire electrodes used for Wire electrical-discharge machining (WEDM): 21 16 29 35 42 24 24 25 Calculate a 99% CI for the variance σ 2 , and the standard deviation σ of the coating layer thickness distribution

99% CI for the variance , and the standard deviation σ of the coating layer thickness distribution is [23.275 , 477.115] and [4.824 , 21.843] respectively.

Step-by-step explanation:

We are given that the following sample observations on total coating layer thickness (in mm) of eight wire electrodes used for Wire electrical-discharge machining (WEDM) : 21, 16, 29, 35, 42, 24, 24, 25

Firstly, the pivotal quantity for 99% confidence interval for the population variance is given by;

                          P.Q. =  ~

where,   = sample variance =  = 67.43

             n = sample of observations = 8

             = population variance

Here for constructing 99% confidence interval we have used chi-square test statistics.

So, 99% confidence interval for the population variance, is ;

P(0.9893 < < 20.28) = 0.99  {As the critical value of chi-square at 7

                                          degree of freedom are 0.9893 & 20.28}  

P(0.9893 < < 20.28) = 0.99

P( < < ) = 0.99

P( < < ) = 0.99

99% confidence interval for = [ , ]

                                                   = [ , ]

                                                   = [23.275 , 477.115]

99% confidence interval for  = [ , ]

                                                  = [4.824 , 21.843]

Therefore, 99% CI for the variance , and the standard deviation σ of the coating layer thickness distribution is [23.275 , 477.115] and [4.824 , 21.843] respectively.

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step-by-step explanation: